Atoms

What you will understand

For NEET UG Physics students: turn an energy-level difference into photon energy, distinguish a cascade from one transition, calculate a head-on Coulomb turning distance and state when a hydrogen-like formula applies.

Jump to chapter practice →

Quick answer: compare states before choosing a formula

An electron level energy is measured relative to a chosen reference. In the elementary hydrogen model, zero is a separated electron at rest infinitely far away; bound levels are negative. A downward transition lowers the electron energy and emits a positive-energy photon equal to the gap. A head-on scattering question instead compares incoming kinetic energy with electric potential energy at a turning point. These are different energy balances, and neither level energy nor a scattering separation is automatically a photon wavelength or a nuclear radius.

Hydrogen levels: a cascade contains separate photon energies

Open full-size diagram ↗

Absorption, excitation and ionisation need distinct endpoints

To excite a hydrogen electron from n=2 to n=3 requires about 1.889 eV in this model. To ionise it from n=2 to the zero-energy continuum requires 3.40 eV. A photon supplies its entire energy in a simple absorption event; it is not an electron projectile that can give only part of an arbitrary kinetic energy to excitation. A collision problem may therefore have a different threshold/energy-sharing interpretation. Specify the initial level and whether the requested final state is bound or ionised.

Rutherford head-on approach: distance is a centre separation

Open full-size diagram ↗

Bohr scaling applies to one-electron systems, with stated approximations

For a one-electron ion of nuclear charge +Ze, the elementary fixed-nucleus model gives $E_n=-13.6Z^2/n^2\,\mathrm{eV}$ and $r_n=a_0n^2/Z$, with supplied a0=0.0529 nm. A hydrogen atom and He+ fit this one-electron idealisation; neutral helium has two electrons and does not obey it directly. Bohr radii are model orbit radii, not general quantum trajectories or the nucleus size. Reduced mass, relativistic effects and detailed spectral structure are outside this elementary scaling.

Series labels depend on the final level

Hydrogen transitions ending at n=1 belong to the Lyman series; those ending at n=2 belong to the Balmer series. The illustrated 3 to 2 line is the approximately 656 nm Balmer line. Classify by the final level, then calculate the energy gap if a wavelength is requested. The name of a series does not mean every member has the same wavelength, and energy levels are not equally spaced.

Common mistakes: keep sign, gap and model separate

A negative bound-level energy does not mean a negative emitted photon energy. Do not use the magnitude of the initial energy when a question asks for a transition between two bound levels. Add photon energies across a cascade, not wavelengths. A head-on Coulomb turn distance is not a nuclear radius. Check that the system has one electron before applying hydrogenic scaling, and do not infer equal radius from equal energy.

Try it: ionisation from an excited level

A hydrogen electron starts at n=2, with model energy −3.40 eV. What minimum energy takes it to the zero-energy continuum? Would using 13.6 eV answer this initial-state question?

Try it: a gap can be shared by different cascade paths

Hydrogen can fall directly from n=3 to n=1, or through n=2. Ignoring recoil, do both routes release the same total photon energy? Must they produce the same number of photons or the same wavelength?

Come back tomorrow: name the states before the gap

Draw three hydrogen levels from memory, label one photon gap and explain why its energy is positive. Then compare two hydrogen-like radii. Revisit NEET Electric Potential and Capacitance for the Coulomb energy reference, or continue to NEET Nuclei to distinguish electronic energy from nuclear binding.

Chapter practice opens the broad Atoms pool.

Sources and review

Technical review: Codex (automated). Primary textbook sources checked on 23 October 2026. Diagrams, worked examples and self-checks are original. Numerical calculations use stated approximations and supplied rounded constants. Human subject review is not claimed. Chapter catalogues and these explanations do not establish complete coverage of every current examination format or syllabus.

Choose your next chapter task

Before the next practice set, write the initial state, final state and quantity requested. After a mistake, correct the model or sign first, then redo the calculation without viewing the solution.

Return to chapter practice and quiz choices →